unit 1; part 2: using factors for fractions and solving problems
DESCRIPTION
Unit 1; Part 2: Using Factors for Fractions and Solving Problems. You need to be able to find the GCF, LCM and solve problems using them. Advanced Homework Answers pp. 199-200. Unit 1, Lesson 9 Advanced – GCF and Simplify Fractions. Assignment – pp. 205-206; - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/1.jpg)
Unit 1; Part 2:Using Factors for
Fractions and Solving Problems
You need to be able to findthe GCF, LCM and solveproblems using them.
![Page 2: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/2.jpg)
Advanced Homework Answerspp. 199-200
3. 9 is not prime. 39. 721. 22 · 32 40. 32
23. 32 · 11 41. 52
25. 2 · 3 · 5 · 7 44. 120 ft2
27. 2 · 32 · 7 45. 23 · 3 · 529. Composite 46. 2 by 3 or 2 by 531. 2 · 2 · 5 · p · q 47. 20 2x3’s or 12 2x5’s33. 7 · 7 · y · y 48. Prime if n = 1; 35. 2 ·2 ·2 ·2 ·3 ·a ·a ·b ·b Composite if n > 1
since 2 is a factor of each.
![Page 3: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/3.jpg)
![Page 4: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/4.jpg)
Unit 1, Lesson 9 Advanced – GCF and
Simplify FractionsAssignment – pp. 205-206;
#9-19 odd, 27, 32, 33, 38, & 40.p. 209; #9-19 odd, #26-28, 30, 32 & 33.
![Page 5: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/5.jpg)
1. GCF is the largest factor that will divide evenly into all the original numbers.
2. Use the ladder to find the GCF.3. Divide by the primes, IN ORDER,
that go into BOTH numbers.
GCF & Simplified Fractions
![Page 6: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/6.jpg)
GCF & Simplified Fractions
Follow the same procedure as before, but look for primes that go into both numbers.
You are through when you run out of common factors.
The numbers down the side are multiplied to make the GCF.
![Page 7: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/7.jpg)
GCF & Simplified Fractions
Two numbers with nothing in common have a GCF of 1.
A simplified fraction has a numerator and a denominator with a GCF of 1.
So, the numbers on the bottom of the ladder make the simplified fraction.
![Page 8: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/8.jpg)
GCF
24 6012 30 6 15
2 5
2))2)3
GCF= 2x2x3=12
24 260 5
![Page 9: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/9.jpg)
GCF
300 18150 9 50 3
2))3
GCF=2x3=6
![Page 10: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/10.jpg)
GCF
625 30125 6
5)
GCF=5
![Page 11: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/11.jpg)
GCF of 3 Numbers
The GCF works the same way with 3 numbers.
You are done when there are no common factors for ALL 3 numbers.
![Page 12: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/12.jpg)
GCF of 3 Numbers
18 42 60 9 21 30 3 7 10
2))3
GCF=2x3=6
![Page 13: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/13.jpg)
GCF of 3 Numbers
56 14 7028 7 35 4 1 5
2))7
GCF=2x7=14
![Page 14: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/14.jpg)
GCF of 3 Numbers
200 120 180100 60 90 50 30 45
10 6 15
2))2)5
GCF=2x2x5=20
![Page 15: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/15.jpg)
GCF of 3 Numbers
12 18 28 6 9 14
2)
GCF=2
![Page 16: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/16.jpg)
GCF of 3 Numbers
32 80 96 16 40 48
8 20 24 4 10 12 2 5 6
2))2)2
GCF=24=16
)2
![Page 17: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/17.jpg)
Find the GCF of 28 and 42.
So, the GCF is 14.
![Page 18: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/18.jpg)
Simplify Fractions• Simplify .
You also can use the old way to simplify.
3075
Answer: 23
![Page 19: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/19.jpg)
Find the GCF of 18 and 45.
Answer: 9
![Page 20: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/20.jpg)
Write in simplest form.
Answer: written in simplest form is
![Page 21: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/21.jpg)
Find the GCF of 20 and 32.
Answer: 4
![Page 22: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/22.jpg)
Write in simplest form.
Answer:
![Page 23: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/23.jpg)
Write in simplest form.
Answer:
![Page 24: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/24.jpg)
Find the GCF of 24 and 36.
Answer: 12
![Page 25: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/25.jpg)
Write in simplest form.
Answer: written in simplest form is
![Page 26: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/26.jpg)
MARBLES In a bag of 96 marbles, 18 of the marbles are black. Write the fraction of black marbles in simplest form.
Answer:
![Page 27: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/27.jpg)
ALGEBRA Find the GCF of
Answer: 7mn
![Page 28: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/28.jpg)
ALGEBRA Find the GCF of 12p2 and 30p3.
Answer: The GCF is 2
Find the GCF of the numbers, then take the highest exponent they have in common.
![Page 29: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/29.jpg)
Find the GCF of 21, 42, and 63.
Answer: The GCF is 3 7, or 21.
![Page 30: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/30.jpg)
Find the GCF of 24, 48, and 60.
Answer: 12
![Page 31: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/31.jpg)
ART Searra wants to cut a 15-centimeter by 25-centimeter piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. What is the length of the side of the squares she should use?The largest length of side possible is the GCF
of the dimensions of the tag board.
The GCF of 15 and 25 is 5.
Answer: Searra should use squares with sides measuring 5 centimeters.
![Page 32: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/32.jpg)
TABLE TENNIS: Rebecca has 20 table tennis balls and 16 paddles. She wants to sell packages of balls and paddles bundled together. What is the greatest number of packages she can sell with no leftover balls or paddles? How many balls and how many paddles will be in each package?
Answer: 4 packages; 5 balls and 4 paddles
![Page 33: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/33.jpg)
TABLE TENNIS: Rebecca (from the last problem) is going to tie the packages with string. If she has 2 yards of string, how many inches of string will she use for each package?
Answer: 18 inches
![Page 34: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/34.jpg)
Note Cards for Unit 1-Lesson 1
1-1. Fraction to DecimalTop divided by bottom.
1-2. Terminating DecimalDivides evenly with no remainder.
1-3. Repeating DecimalDecimal places repeat over and
over.1-4. Bar Notation
A line over decimals to show that they repeat.
![Page 35: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/35.jpg)
![Page 36: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/36.jpg)
![Page 37: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/37.jpg)
Advanced Homework Answerspp. 205-206 & 209
9. 6 38. D 26. 1/411. 5 40. 10s 27. 3/413. 24 9. 5/7 28. 2/1515. 8 11. 7/10 30. A17. 6 13. 4/7 32. 2319. 7 15. 6/7 33. 2 · 32 · 5 · 727. 9b 17. 132. 4 inches 19. 5/633. No only 16 4” pieces–need 18
![Page 38: Unit 1; Part 2: Using Factors for Fractions and Solving Problems](https://reader036.vdocuments.net/reader036/viewer/2022062323/568165d0550346895dd8dd1e/html5/thumbnails/38.jpg)